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Given
T->"time period of revolution"= 90min=5400s
h-> " height of the orbit"=280km
R->"radius of the earth is at the equator" =6400 km
Let
m-> " mass of the satellite"
M-> " mass of the earth"
G-> " Gravitational constant"
g-> " acceleration due to gravity"=9.8ms^-2
v-> " speed of the satellite at height h"
Considering the gravitational pull on satellite when it is on the surface of the earth we can write
G(mM)/R^2=mg
=>GM=gR^2.........(1)
Again considering the gravitational pull on satellite when it is revolving round the earth in an an orbit at height h in the equatorial plane with speed v , we can write
G(mM)/(R+h)^2=(mv^2)/(R+h)
=>(GM)/(R+h)=v^2
Now replacing GM=gR^2
=>(gR^2)/(R+h)=v^2
=>v=Rxxsqrt(g/(R+h))=6400kmxxsqrt((9.8xx10^-3kms^-2)/((6400+280)km))
=>v=(64xx7)/sqrt3340kms^-1~~7.75kms^-1
